- Philip Griffiths Professor of Mathematics
- Professor in the Department of Mathematics
Tuesdays and Thursdays, 10:30-12:00PM, and by appointment
Research Areas and Keywords
Algebra & Combinatorics
Geometry: Differential & Algebraic
PDE & Dynamical Systems
I'm interested in the geometry of partial differential equations (as always), but, more specifically, I have been thinking about conservation laws for PDE, Finsler geometry, calibrations, holonomy, and trying to learn more about Seiberg-Witten invariants and symplectic geometry.
Most recently, I have been named as the Director of the Simons Collaboration "Special Holonomy in Geometry, Analysis, and Physics", and so most of my research lately and in the near future will be directed towards problems in this area.
Berger, E, and Griffiths, P. "The Gauss equations and rigidity of isometric embeddings." Duke Math. J. 50.3 (1983): 803-892.
Griffiths, P, and Yang, D. "Characteristics and existence of isometric embeddings." Duke Math. J. 50.4 (1983): 893-994.
Bryant, RL. "Conformal and minimal immersions of compact surfaces into the 4-sphere." J. Differential Geom. 17.3 (1982): 455-473. (Academic Article)
Bryant, RL. "Submanifolds and special structures on the octonians." J. Differential Geom. 17.2 (1982): 185-232.
Bryant, RL. "Holomorphic curves in Lorentzian CR-manifolds." Trans. Amer. Math. Soc. 272.1 (1982): 203-221.
Berger, E, and Griffiths, P. "Some isometric embedding and rigidity results for Riemannian manifolds." Proc. Nat. Acad. Sci. U.S.A. 78.8 (1981): 4657-4660.
Bryant, RL. "Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms." Adv. Stud. Pure Math., 37, Math. Soc. Japan, Tokyo, 2002, 1--44. Open Access Copy
Bryant, RL, Dunajski, M, and Eastwood, M. "Metrisability of two-dimensional projective structures." Open Access Copy